Cooled - as in 1l of water left in a properly insulated container for no more than 30 mins - will give you not boiling but still very hot (70C ish) water. Bugs get killed above 65C unless they're extremely lucky! If it's boiling then it can clag up the powder and there's a risk you might scald yourself so 70C is a good compromise.
The 30 minutes guidance is based on the specific heat capacity of 1l of water, not that they tell you this on the packet, they just mention boiling water and leaving it to cool for 30mins without explaining why.
Cold boiled water (room temp) does nothing. If it's not hot to touch it's not hot enough to kill bugs.
Remener it's not the water that needs to be sterilised, tap water in the UK is perfectly safe as of 6m and before that it only really needs boiling to make sure all the chlorine, which is what makes it safe, has evaporated.
The risk is from the powder which can be contaminated during the manufacturing process or while being opened and closed in your kitchen. Salmonella and C. sakazakii are the big ones to watch out for but many people are passive carriers of some quite nasty bacteria, like MRSA in basal passages, so if you sneeze and the powder is open those bugs can settle in the powder and breed quite happily because powdered milk is a great growth medium for babies and bugs alike! So the water needs to be hot to sterilise the powder when the powder is mixed because the powder can't be pasteurised like a ready made carton can.
The safest way is to make each bottle fresh by pouring out the correct amount of hot water, then adding the powder, then cooling it under a cold tap to use instantly.
The next safest is to make batches as above and store them under 5C, in the back of the fridge, for less than 24 hours.
A marginally more fiddly but still safe method is to divide the amount of water in half, so for a 6oz bottle which usually uses 6scoops of powder you'd need 3oz and 3oz, and add all the powder to 3oz of hot water and shaking thoroughly to disperse all the powder. You then top up with the 3oz of cold water to bring it down to drinkable temp quickly and shake again.
Does that make sense?